# The empty-set as a subset, and as a member

Reading the Hammack 'Book of Proof'.

He shows that the empty-set is a subset of all possible sets.

I believe this doesn't also mean that the empty-set is also a member of all possible sets.

Is my understanding correct?

• This is correct. For example, $\varnothing \subset\{1\}$ but $\varnothing\notin\{1\}$. – Gyu Eun Lee Nov 15 '16 at 6:01

Yes, you are correct. Consider the following sets: $A = \{1,2\}$ and $B = \{\emptyset, 1,2\}$. Note that $\emptyset \in B$ and $\emptyset \in B-A = \{\emptyset\}$ but $\emptyset \not\in A$, even though $\emptyset$ is a subset of all the above sets.